Question

six dogs pull a two-person sled with a total mass of 220 kg . the coefficient of kinetic friction between the sled and the snow is 0.080. the sled accelerates at 0.65 m/s2 until it reaches a cruising speed of 11 km/h . part a what is the team's maximum power output during the acceleration phase? express your answer with the appropriate units.

Answer 1

Main Answer:

The team's maximum power output during the acceleration phase is 8440 W.

Step-by-step explanation:

The power output of the dog sled team can be determined using the equation
`\( P = F \cdot v \)`, where
`\( P \) is power, \( F \)`is force, and
`\( v \)` is velocity. During acceleration, the net force acting on the sled is the difference between the applied force by the dogs and the force of kinetic friction opposing their motion. The applied force is given by
`\( F_{\text{applied}} = m \cdot a \), where \( m \)` is the total mass of the sled and \( a \) is the acceleration. The force of kinetic friction is
`\( F_{\text{friction}} = \mu_k \cdot N \), where \( \mu_k \)` is the coefficient of kinetic friction and
`\( N \)` is the normal force.

Now, the net force is
`\( F_{\text{net}} = F_{\text{applied}} - F_{\text{friction}} \). Substituting in the values given (mass \( m = 220 \ \text{kg} \),`acceleration
`\( a = 0.65 \ \text{m/s}^2 \),`and coefficient of kinetic friction
`\( \mu_k = 0.080 \)),` we find the net force. Finally, the power is calculated using
`\( P = F_{\text{net}} \cdot v \), where \( v \)` is the cruising speed converted to meters per second. The result is a maximum power output of 8440 W.

In summary, the team's power output during acceleration is the difference between the applied force and the force of friction, with all relevant values plugged into the appropriate equations. This calculation gives us insight into the physical demands placed on the sled team during the acceleration phase.

Answer 2

The team's maximum power output during the acceleration phase is 1900 W, determined by overcoming gravitational force (mg) and kinetic friction (μkN). This is calculated by multiplying the net force by the sled's acceleration and adjusting for cruising speed in meters per second.

Step-by-step explanation:

The team's maximum power output during the acceleration phase is determined by the opposing forces acting on the sled. As the six dogs exert force to accelerate the sled, they must overcome both gravitational pull and kinetic friction. The force due to gravity is represented by the product of the mass (m) and gravitational acceleration (g), commonly denoted as mg. Additionally, the force opposing the sled's motion due to kinetic friction is calculated as μkN, where μk is the coefficient of kinetic friction, and N is the normal force.

The net force acting against the sled's acceleration is the sum of these two forces (mg + μkN). Multiplying this net force by the acceleration of the sled (0.65 m/s²) yields the power exerted by the team. To express the final answer in watts, the product is then multiplied by the sled's velocity during the acceleration phase.

The conversion of the cruising speed to meters per second ensures consistency in the units used. The result, 1900 watts, signifies the maximum power output of the team during the acceleration phase of sled pulling. This calculation encapsulates the intricate interplay of gravitational forces and friction, showcasing the physical principles governing the dynamic process.